Opie's Job - S6-E1
Other mistake: In the scenes outside the grocery store with Mr. Doakes, there are a couple dozen cereal boxes in the display windows - Post Grape Nuts, Post Grape Nuts Flakes, Post Alpha Bits, etc., and all the boxes have part of their names covered, such as "Rap Ut." It's pretty funny considering that TAGS cast did commercials for Post Grape Nuts, and other Post foods.
Andy's Rival - S6-E2
Other mistake: After Helen calls Andy to cancel their date, it cuts to Goober and Andy walking down the street and there's a brick wall adjacent to the grocery/meat store which should not exist.
Other mistake: When John Canfield's talking to Floyd, Andy, and the other men they're in front of the display window, which doesn't have any panes of glass.
Other mistake: While Andy and Helen are rearranging everything in the squad car's trunk to make it all fit, Helen picks up the large thermos and written on its bottom we see "Reggie personal." Reggie Smith was property master on set. (00:12:45)
Other mistake: During the scenes at Goober's filling station we can see a few brand names covered. For example, the "Chew Mail Pouch Tobacco" wall thermometer sign has its brand name "Mail Pouch" covered with black tape, and all the yellow "Pennzoil" cans have half the letters of their brand name painted yellow, so all the cans read "en zo."
Aunt Bee Learns to Drive - S6-E21
Other mistake: Aunt Bee says that Andy had to drive her to Clara's and Andy says it's not a bother, but Clara has always lived right next door.
Answer: It was a joke. They were supposed to be dumb hillbillies.
Both. According to later interviews with both Andy and the Dillards band (the real name of the band that played the parts of the Darling children, of which Charlene (Maggie Peterson - Mancuso was also a member) the reason the Darling boys never had any lines was because they would've had to have been paid if they spoke. In return for appearing without lines or pay, Andy promised to get as much of their music onto the show as possible which, he did. This obviously gave them a lot of exposure.